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Derivative of:
Derivative of (x^2+49)/x
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Derivative of (x-3)/sqrt(x)
Integral of d{x}:
1/(1+x^5)
Identical expressions
one /(one +x^ five)
1 divide by (1 plus x to the power of 5)
one divide by (one plus x to the power of five)
1/(1+x5)
1/1+x5
1/(1+x⁵)
1/1+x^5
1 divide by (1+x^5)
Similar expressions
1/(1-x^5)

The derivative of the function/ 1/(1+x^5)

Derivative of 1/(1+x^5)

The solution

You have entered [src]

  1   
------
     5
1 + x

$$\frac{1}{x^{5} + 1}$$

1/(1 + x^5)

Detail solution

Let $u = x^{5} + 1$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{5} + 1\right)$ :
1. Differentiate $x^{5} + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
  The result is: $5 x^{4}$
The result of the chain rule is:

$- \frac{5 x^{4}}{\left(x^{5} + 1\right)^{2}}$

The answer is:

$- \frac{5 x^{4}}{\left(x^{5} + 1\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      4  
  -5*x   
---------
        2
/     5\ 
\1 + x /

$$- \frac{5 x^{4}}{\left(x^{5} + 1\right)^{2}}$$

Simplify

The second derivative [src]

      /         5 \
    3 |      5*x  |
10*x *|-2 + ------|
      |          5|
      \     1 + x /
-------------------
             2     
     /     5\      
     \1 + x /

$$\frac{10 x^{3} \left(\frac{5 x^{5}}{x^{5} + 1} - 2\right)}{\left(x^{5} + 1\right)^{2}}$$

Simplify

The third derivative [src]

      /           10        5 \
    2 |       25*x      20*x  |
30*x *|-2 - --------- + ------|
      |             2        5|
      |     /     5\    1 + x |
      \     \1 + x /          /
-------------------------------
                   2           
           /     5\            
           \1 + x /

$$\frac{30 x^{2} \left(- \frac{25 x^{10}}{\left(x^{5} + 1\right)^{2}} + \frac{20 x^{5}}{x^{5} + 1} - 2\right)}{\left(x^{5} + 1\right)^{2}}$$

Simplify

7-я производная [src]

         /            15          25         5          10          20\
       3 |     31250*x     15625*x     1215*x    10500*x     37500*x  |
25200*x *|24 - --------- - --------- - ------- + --------- + ---------|
         |             3           5         5           2           4|
         |     /     5\    /     5\     1 + x    /     5\    /     5\ |
         \     \1 + x /    \1 + x /              \1 + x /    \1 + x / /
-----------------------------------------------------------------------
                                       3                               
                               /     5\                                
                               \1 + x /

$$\frac{25200 x^{3} \left(- \frac{15625 x^{25}}{\left(x^{5} + 1\right)^{5}} + \frac{37500 x^{20}}{\left(x^{5} + 1\right)^{4}} - \frac{31250 x^{15}}{\left(x^{5} + 1\right)^{3}} + \frac{10500 x^{10}}{\left(x^{5} + 1\right)^{2}} - \frac{1215 x^{5}}{x^{5} + 1} + 24\right)}{\left(x^{5} + 1\right)^{3}}$$

Simplify

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Derivative of 1/(1+x^5)

The graph:

Piecewise:

The solution